Question

Find maxima and minima of function f(x)= x³ - 18x² + 33x​

Answer 1

Answer:

f(x) = x³ - 18x² + 33x​

f'(x) = 3x² - 36x + 33

f'(x) = 0

=> 3x² - 36x + 33 = 0

=> x^2 - 12x + 11 = 0

(x - 11)(x - 1) = 0

x = 1, 11.

f''(x) = 6x - 36

Now, if x = 1, f''(x) = -30 <0

if x = 11, f''(x) = 30 >0

We know, that if f''(x) <0, f(x) is the maxima, while if f''(x) >0, f(x) is the minima.

So, at x = 1, it is maxima, while at x = 11, it is minima.

So maximum value = 1 - 18 + 33 = 16

    minimum value = 1331 - 2178 + 363 = -494